The present invention relates to a photon beam generating apparatus for generating two photon beams containing photons generated simultaneously and constituting a photon pair, and to a photon beam generating apparatus capable of determining the time of generation of the photons included in the photon beams. The photon beam generating apparatus according to the present invention can be used in a quantum cryptographic communications system, a quantum computation system, an analysis system, or a like system.
If photons constituting a pair can be produced simultaneously, the time and the position at which one of the paired photons is present can be determined through measurement of the other photon. In general, such a pair of photons having high temporal correlation is generated through generation of a parametric fluorescence pair.
A parametric fluorescence pair is constituted of two photons {overscore (h)}xcfx89i and {overscore (h)}xcfx89s produced when a photon having an energy of {overscore (h)}xcfx890 enters a non-linear optical medium. In this case, {overscore (h)} represents a value obtained through division of Planck""s constant h=6.62xc3x9710xe2x88x9234 [jxc2x7s] by 2xcfx80. xcfx89s, and xcfx890 respectively represent the frequency of a signal beam, the frequency of an idler beam, and the frequency of an incident photon (xe2x80x9csignal beamxe2x80x9d and xe2x80x9cidler beamxe2x80x9d are conventional names representing respective photons in each photon pair). Also, according to the law of conservation of energy, the following relation is satisfied:
xcfx890=xcfx89i+xcfx89s.xe2x80x83xe2x80x83(1)
In addition, the following relation with regard to conservation of momentum is satisfied:
{overscore (h)}k0={overscore (h)}ki+{overscore (h)}ksxe2x80x83xe2x80x83(2)
where ks, ki, and k0 respectively represent the frequency of the signal beam, the frequency of the idler beam, and the frequency of the incident photon beam. Equations (1) and (2) are called phase-matching conditions. In order to produce parametric fluorescence pairs, the phase-matching conditions must be satisfied within a medium having a sufficient non-linear constant.
FIG. 14 shows an example of a conventional technique utilizing parametric fluorescence pairs described in Sergienko et. al, Journal of Optical Society of America B, May 1995, Vol. 12, No. 5, pp 859, xe2x80x9cExperimental Evaluation of a Two-Photon Wave Packet in Type-II Parametric Downconversion.xe2x80x9d
In FIG. 14, reference numeral 13 denotes an argon laser, 14 denotes an incident pump beam, 15 denotes a dispersion prism, 25 denotes a BBO crystal, 31 denotes a dispersion prism, and 32 denotes a parametric fluorescence beam. Although the experiment was conducted for measurement of time correlation between produced photons constituting a pair, in FIG. 14, portions other than the portion used for generation of photon beams are omitted for simplicity.
The argon laser 13 produces a single frequency UV laser beam (having a wavelength of 351.1 nm) serving as the incident pump beam 14. The dispersion prism 15 is used for eliminating components other than the component having a wavelength of 351.1 nm from the beam generated by the argon laser. When the incident pump beam 14 enters the BBO crystal 25, parametric fluorescence pairs are produced therein. In the experiment, the angle between the crystal axis of the BBO crystal 25 and the incident pump beam 14 is set at 49.2 degrees in order to satisfy a collinear condition. The collinear condition specifies that the wave number vector of the incident pump beam 14 is parallel with the wave number vectors of the produced fluorescence pairs. The details of the collinear condition will be described in greater detail in the embodiments of the present invention. Because the produced parametric fluorescence beams 32 travel along the axis of the incident pump beam 14, the fluorescence beams 32 are separated from the incident beam 14 by the dispersion prism 31 before being used.
The collinear condition is used not only in the example described above but also in a wide range of experiments related to generation of parametric fluorescence pairs. The reason for this is as follows. When an optical system is constructed, the tilt angles and the positions of optical components are adjusted on the basis of observation of an image of a standard laser beam or an image of the standard laser beam reflected from a surface of each optical component. Generally, since the parametric fluorescence light is of extremely low intensity, a special device such as a cooled CCD must be employed in order to detect the position and the direction of propagation of the produced light. Thus, construction of an experimental system becomes difficult. However, under the collinear condition, a UV pump beam and generated fluorescence pairs propagate collinearly and in the same direction. Consequently, by setting a reference laser beam, which has a wavelength close to that of the fluorescence light, coaxial with the UV pump beam, construction of the experiment system becomes relatively easy.
However, generation of fluorescence pairs under the collinear condition has involved a major drawback. Under the collinear condition, the parametric fluorescence light is emitted over a wide angular range (6.5 degrees in the example). Accordingly, fluorescence pairs radiated in the same direction as the UV pump beam, which are used in the experiment, constitute only a portion of the fluorescence pairs which are actually produced. Consequently, in a conventional optical system:
1. it is difficult to convert the portion of the fluorescence pairs into a beam which has a circular or oval cross-section and which can be used easily;
2. it is difficult to cut out or select a pair of photons radiated in correlated directions; and
3. the quantity of the parametric fluorescence light per unit radiation angle is small.
The reasons for the cause of the above-mentioned difficulties and drawbacks will now be described in detail.
FIG. 15 shows results of calculation performed with regard to the radiation angles of parametric fluorescence pairs under the collinear condition, described in xe2x80x9cProposal for a Loophole-Free Bell Inequality Experiment,xe2x80x9d Paul G. Kwiat, et. al., Physical Review A, Vol. 49, No. 5, (1994) pp 3209.
FIG. 15 is a plot showing radiation angles of fluorescence pairs with respect to the UV pump beam that enters the crystal in a direction perpendicular to the sheet of FIG. 15 from the back thereof. The optical axis of the crystal is directed upward in FIG. 15. Each hollow triangle indicates the radiation angle of an extraordinary-polarized fluorescence beam and each hollow circle indicates the radiation angle of an ordinary-polarized fluorescence beam. The hollow triangle and the hollow circle are both present at the origin, where the collinear condition is satisfied. As can be seen from the plot, under the collinear condition, the fluorescence pairs are radiated over a wide angular range. Accordingly, as has been described, in a case where only a portion of the fluorescence pairs radiated in the same direction as the UV pump beam is used, as in conventional experiments, the following difficulties arise.
1. As can be seen from FIG. 15, when fluorescence pairs radiated in the same direction as the UV pump beam are used, the fluorescence pairs are cut out as a portion of an arc as shown in the photographs of FIG. 8. It is difficult to convert the thus-cut-out portion of the fluorescence pairs into a beam having a circular or an oval cross-section without involving a reduction in light intensity. Moreover, if the cut-out portion is converted as such by the use of a suitable pinhole, the number of useable fluorescence pairs decreases due to a loss produced at the pinhole.
2. Photons of a generated fluorescence pair are radiated to positions that are symmetric with respect to the origin in the plot of FIG. 15. Accordingly, in order to obtain paired fluorescence beams each containing most of the generated photons (i.e., having a high correlation), photon pairs must be cut out or selected carefully with attention to their symmetry with respect to the origin, which is a difficult task.
3. For example, in the experiment described in the above-mentioned literature Sergienko et. al, Journal of Optical Society of America B, May 1995, Vol. 12, No. 5, pp 859, xe2x80x9cExperimental Evaluation of a Two-photon Wave Packet in Type-II Parametric Downconversion,xe2x80x9d only 20 fluorescence pairs per second are available. This is mainly because only a portion of the fluorescence pairs that emerged from the crystal can be used.
Conventionally, since a portion of parametric fluorescence pairs which are radiated over a wide angular range is used, it is difficult to convert the portion into a beam having a circular or an oval cross-section, and it is also difficult to cut out or select photons radiated in mutually-correlated directions. Moreover, the light energy of the parametric fluorescence light per unit radiation angle is small.
The present invention has been accomplished in order to solve such problems. An object of the present invention is to produce parametric fluorescence pairs which are radiated within a small solid angle and which can be easily converted into a beam having a circular or an oval cross-section. Another object of the present invention is to increase the quantity of the parametric fluorescence light per unit radiation angle through a decrease in the radiation angle of parametric fluorescence pairs.
(1) A photon beam generating apparatus of the present invention comprises an incident pump beam generation section and a photon pair generation section including a non-linear optical medium. The angle between the optical axis of the medium and an incident pump beam is set to a value such that tuning curves become tangent to a line corresponding to a wavelength a in order to generate two photon beams including paired photons generated simultaneously and having a wavelength a.
(2) Another photon beam generating apparatus of the present invention comprises an incident pump beam generation section and a photon pair generation section including a non-linear optical medium. The angle between the optical axis of the medium and the incident pump beam is set to a value such that tuning curves become tangent to different lines corresponding to wavelengths a and b respectively, in order to generate two photon beams including paired photons generated simultaneously and having wavelengths a and b respectively.
(3) Moreover, in addition to the photon pair generation section as described above, the photon beam generating apparatus of the present invention comprises a detection section for detecting one of the produced photons constituting a pair.
(4) Furthermore, in addition to the photon pair generation section as described above, the photon beam generating apparatus of the present invention comprises lenses converging the respective photon beams produced by the photon pair generation section, and optical fibers through which the photon beams propagate.
(5) Still further, in addition to the photon pair generation section as described above, the photon beam generating apparatus of the present invention comprises optical fibers through which the produced photon beams propagate.
The photon beam generating apparatus according to the present invention having the configuration as described above operates as follows.
(1) In the present invention, when an incident pump beam from the incident pump beam generation section enters the photon pair generation section, there are generated two photon beams having a small angular deviation and including paired photons produced simultaneously and each having a wavelength a.
(2) Additionally, in the present invention, when an incident pump beam from the incident pump beam generation section enters the photon pair generation section, there are generated two photon beams having a small angular deviation and including paired photons produced simultaneously and having wavelengths a and b respectively.
(3) Moreover, in the present invention, through detection of one beam including one of the paired photons generated by the photon pair generation section, the time of production of each photon included in the other photon beam is determined.
(4) Furthermore, in the present invention, in order to efficiently transmit photon beams produced by the photon pair generation section to the optical fibers, each of the lenses converges the respective photon beam before the beam enters an optical fiber.
(5) Still further, in the present invention, in order to efficiently transmit photon beams produced by the photon pair generation section to the optical fibers, each of the photon beams enters an optical fiber directly.